Isospectrality for quantum toric integrable systems

Details Isospectrality for quantum toric integrable systems Isospectrality for quantum toric integrable systems

2011-11-25

arxiv.org/abs/1111.5985v1

Mathematics

Symplectic Geometry

35 pages, 6 figures

Scientific paper

We settle affirmatively the isospectral problem for quantum toric integrable systems: the semiclassical joint spectrum of such a system, given by a sequence of commuting Toeplitz operators on a sequence of Hilbert spaces, determines the classical integrable system given by the symplectic manifold and Poisson commuting functions, up to symplectomorphisms. We also give a full description of the semiclassical spectral theory of quantum toric integrable systems. This type of problem belongs to the realm of classical questions in spectral theory going back to pioneer works of Colin de Verdiere, Guillemin, Sternberg and others in the 1970s and 1980s.

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